Advantage and disadvantage of gauss's interpolation formula
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Excellent answers are given, just an addendum.
One must make sure that this least squares approximation is applicable.
If you want to investigate the relation between two variables a least squares approximation assumes that there is a causal relationship between them.
Because these squares are calculated for the dependent variable only, it matters which variable is assumed to be (in)dependent.
This means that it can be used to predict the dependent variable, given a value of the independent variable. But this can not simply be reversed, or at least one has to be careful in estimating the error you make in your prediction when you do. This application of using a least squares approximation is used a lot in practice. Calibration is one example.
It also means that if there is no causal relationship, one would prefer a method which does not ‘favour’ any of the variables involved. I'm not an expert, but orthogonal regression springs to mind.
One must make sure that this least squares approximation is applicable.
If you want to investigate the relation between two variables a least squares approximation assumes that there is a causal relationship between them.
Because these squares are calculated for the dependent variable only, it matters which variable is assumed to be (in)dependent.
This means that it can be used to predict the dependent variable, given a value of the independent variable. But this can not simply be reversed, or at least one has to be careful in estimating the error you make in your prediction when you do. This application of using a least squares approximation is used a lot in practice. Calibration is one example.
It also means that if there is no causal relationship, one would prefer a method which does not ‘favour’ any of the variables involved. I'm not an expert, but orthogonal regression springs to mind.
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